Development and Testing of a Minaturized,

Dual-Frequency GPS Receiver for Space Applications

Andrew J. Joplin, The University of Texas at AustinE. Glenn Lightsey, The University of Texas at Austin

Todd E. Humphreys, The University of Texas at Austin

BIOGRAPHIES

Andrew J. Joplin is a graduate student in the depart-ment of Aerospace Engineering and Engineering Me-chanics at the University of Texas at Austin. He re-ceived a B.S. in Aerospace Engineering, with an em-phasis on Space Flight, from the University of Texasat Austin. His interests are in the areas of orbitalmechanics, orbit determination, and GNSS technologyand applications.

E. Glenn Lightsey is a professor in the Departmentof Aerospace Engineering and Engineering Mechanicsat the University of Texas at Austin. He received aB.S.E. from Princeton University, an M.S. from TheJohns Hopkins University, and a Ph.D. from Stan-ford University. His research involves small satellitetechnology, including: guidance, navigation, and con-trol; attitude determination and control; formation fly-ing, satellite swarms, and satellite networks; coopera-tive control; proximity operations and spacecraft ren-dezvous; space based GNSS; visual navigation; propul-sion; satellite operations; and space systems engineer-ing.

Todd E. Humphreys is an assistant professor in thedepartment of Aerospace Engineering and EngineeringMechanics at the University of Texas at Austin. Hereceived a B.S. and M.S. in Electrical and ComputerEngineering from Utah State University and a Ph.D.in Aerospace Engineering from Cornell University. Hisresearch interests are in estimation and filtering, GNSStechnology, GNSS-based study of the ionosphere andneutral atmosphere, and GNSS security and integrity.

ABSTRACT

Dual-frequency space-based GPS receivers have manymission-enabling capabilities as compared to theirsingle-frequency counterparts. The ionosphere-corrected range measurement allows precise orbit de-termination (POD) of the spacecraft to centimeterlevel, which has been successfully demonstrated inseveral space missions that have studied the Earth.Furthermore, the dual-frequency measurement allowsobservation of the ionospheric delay, which supportsGPS radio occultation and space weather experiments.With the emergence of a second civilian GPS signal,dual-frequency measurements may be used for futurereal-time space applications such as autonomous for-mation flying, satellite networks, and cooperative con-trol (e.g., satellite inspection and rendezvous).

While dual-frequency GPS receivers have been usedin space for more than two decades, the size, power,and cost of this technology is an important driverfor future space missions. The growing availability oflaunch opportunities for very small satellites known asnanosatellites and CubeSats raises the possibility ofmore affordable access to space measurements if theobservation quality is sufficient to support the user’sneeds.

This paper presents the initial development and test-ing of the Fast, Orbital, TEC, Observables, and Nav-igation (FOTON) receiver: a small, reconfigurable,dual-frequency, space-based GPS receiver. Originallydeveloped as a science-grade software receiver for mon-itoring ionospheric scintillation and total electron con-tent (TEC), this receiver was designed to provide high-quality GPS signal observations. The original receiverhardware was miniaturized and the software has beenadapted for low earth orbit (LEO) operations. FO-

TON now fits within a 0.5U CubeSat form factor (8.3x 9.6 x 3.8 cm), weighs 400 g, and consumes 4.5 Wof instantaneous power, which can be reduced to ¡1W orbit average power with on-off duty cycling. Thereceiver has been designed with commercial parts tokeep manufacturing costs low.

Significant testing of FOTON has been performed withlive signals and with signals generated by a SpirentGPS signal simulator. Initial terrestrial tests demon-strate behavioral consistency with the original heritagehigh performance receiver. Several LEO simulationsare presented, demonstrating FOTON’s single- anddual-frequency positioning, Kalman filter based POD,and GPS radio occultation observation capabilities. Inaddition, its acquisition and reacquisition performanceis presented; on average, FOTON’s time to first fix isapproximately 45 seconds. Finally, an orbital Kalmanfilter is introduced to enable navigation in geostation-ary orbit (GEO), which is a challenging applicationfor space- based GPS navigation. Extensive testingdemonstrates that FOTON is a robust, versatile, high-precision dual-frequency space receiver. Its low cost,size, weight, and power requirements are key enablersfor future small-satellite missions.

1 INTRODUCTION

The position, velocity, and timing (PVT) requirementsfor satellites varies according to the mission. Somesatellites, such as some of the student-built CubeSatsdeveloped by the University of Texas at Austin (UT-Austin) Satellite Design Laboratory, require only verycoarse navigation capability. Major space science mis-sions, however, often require precise (sub-meter) navi-gation. One example is the Gravity Recovery and Cli-mate Experiment (GRACE), which uses K-band rangemeasurements to detect changes in Earth’s local grav-itational field [1]. This requires high-precision knowl-edge of the GRACE satellites’ positions. Some smallsatellite missions (such as FASTRAC [2]) involve rela-tive navigation of two satellites, and could lead to au-tomated rendezvous and docking demonstrations. Thehigher precision required for such goals can be attainedusing dual-frequency GPS receivers.

Another use for dual-frequency receivers on satellitesis ionospheric research. A typical ionospheric researchmission, such as the Constellation Observing Systemfor Meteorology, Ionosphere, and Climate (COSMIC)mission [3], involves relatively large, expensive satel-lites. If such a mission could be accomplished usingCubeSats, the science return per dollar spent would

be significantly higher.

This paper focuses on such navigation and scientificapplications of space-based GPS receivers, with spe-cial attention given to small satellite applications. Itpresents a small, dual-frequency receiver that is underdevelopment, and is expected to be the primary nav-igation sensor on UT’s upcoming ARMADILLO mis-sion. The Fast, Orbital, TEC, Observables, and Nav-igation (FOTON) receiver (Fig. 1) is a miniaturizedversion of a dual-frequency terrestrial science receiverdeveloped by Cornell University and The University ofTexas at Austin.

As part of this research, changes have been madeto FOTON’s software to allow it to navigate in themore challenging environment of space. Some addi-tions have also been made to the software to improveits performance, including an orbital Kalman filter tosupplement the existing point solution algorithm. Theresults of considerable testing are also presented todemonstrate FOTON’s capabilities in a variety of sce-narios, including both static and simple dynamic ter-restrial tests, single- and dual-frequency low Earth or-bit (LEO) tests, and a geosynchronous orbit (GEO)test.

Figure 1 FOTON Receiver

The next section presents a brief overview of softwarereceivers in general, and FOTON specifically. It alsosummarizes the major changes that needed to be madein order for FOTON to navigate on orbit, most ofwhich were either discovered or verified by the test-ing presented in Section 3. In addition to describingthe setup and procedures used in testing FOTON, Sec-tion 3 presents the results of the initial characteriza-tion of the CASES and FOTON receivers, comprisinga live-sky test, static and dynamic terrestrial simu-

lations, and two LEO simulations. Section 4 exam-ines FOTON’s signal acquisition and reacquisition per-formance as a precursor to an in-depth duty cyclingstudy. This is followed in Section 5 by a description ofa LEO extended Kalman filter designed by the author.This filter provides a core capability that can be laterimproved to make possible sub-meter precision orbitdetermination. Section 6 presents the results of theinitial dual-frequency LEO simulation testing; it com-pares several single- and dual-frequency configurationsto illustrate FOTON’s dual-frequency navigation per-formance. This is followed by a brief overview of radiooccultation and an example of how FOTON can beused to measure entire local ionospheric delay profiles.Finally, Section 8 demonstrates FOTON’s navigationcapability in a geosynchronous orbit simulation, an ac-complishment made possible through the use of a high-precision timing reference and the reconfigurability ofa software receiver.

2 BACKGROUND

FOTON is a dual-frequency, software-defined GPS re-ceiver adapted from the Connected Autonomous SpaceEnvironment Sensor (CASES) receiver developed byCornell University and The University of Texas atAustin. The CASES receiver consists of a radiofrequency (RF) front end, a single-board computer(SBC), and a digital signal processor (DSP) chip. Thesoftware that runs on CASES is the GNSS ReceiverImplementation on a DSP (GRID) code, written inC++. FOTON, the space-based version of the re-ceiver, uses the same hardware as CASES, repackagedto fit within a 0.5U CubeSat volume (approximately8.3×9.6×3.8 cm). FOTON runs an altered version ofthe GRID code that was developed in this researchand works in low earth orbit. This section discussesthe advantages of software receivers in general, andprovides a brief overview of the original GRID code,the CASES receiver, and FOTON. A summary of thechanges required to make FOTON function in LEO isalso provided.

2.1 Software Receivers

Traditional GPS receivers are composed of general-purpose processors and application-specific integratedcircuits (ASICs). The signal correlation is performedon ASICs, while tracking and navigation are performedon the processor. This is acceptable in most cases,because there is often no reason to make changes to

the receiver. Software-defined receivers, however, in-gest raw digital signals from a data acquisition (DAQ)board and perform correlation as well as tracking andnavigation on a general-purpose processor.

Software-defined receivers have recently been gainingpopularity due to the ease with which any part of thereceiver, from navigation all the way down to corre-lation, can be changed. This allows for significantlydecreased development time, as well as greater re-ceiver customization. When considering space-basedGPS receivers, this advantage becomes even more pro-nounced; if a bug is found in the receiver when it is al-ready on-orbit, or if additional functionality is desired,the same satellite may still be used by simply upload-ing new software to the receiver. As will be demon-strated in Chapter 8, the ability to make changes toa receiver’s correlation opens up the possibility of us-ing a single receiver design for geosynchronous orbitpositioning in addition to terrestrial and low Earthorbit positioning. While it is true that software re-ceivers, in general, have higher power requirementsthan their hardware-based counterparts, the recent ad-vancements in microprocessor technology renders thisdisadvantage insignificant compared with the flexibil-ity offered by software receivers.

2.2 GRID Code

The GRID code processes a stream of binary, interme-diate frequency (IF) sign, magnitude, and clock datafrom an RF front end, tracking GPS L1 C/A and L2Csignals, and producing a navigation solution (see Fig.2). The data can be input to a DSP in real-time fromthe front end, or it can be recorded and used as in-put to the equivalent post-processing receiver (PpRx).PpRx is a post-processing implementation of GRID,designed to be compiled and run on any Linux com-puter. It shares most of the same code as the real-time,DSP-based receiver, so the only difference in behaviorshould be run-time speed.

Figure 2 Schematic Representation of GRID [4]

The GRID code is designed to take advantage ofthe object-oriented programming capabilities of C++.

Signal tracking is handled by two main classes: Bank

and Channel, both fully configurable. The Bank classcontains all of the information required for tracking aspecific signal type, such as L1 C/A or L2C. AlthoughGRID is capable of tracking other signal formats, suchas L5 and other CDMA signals, this report will fo-cus on L1 C/A and L2C only. The Channels containloop and observables information for each signal beingtracked within a Bank.

2.3 CASES and FOTON Receivers

The CASES receiver is constructed from commercial,off-the-shelf (COTS) components on custom-built cir-cuit boards (Fig. 3). The FOTON receiver is a mina-turized version of CASES (Fig. 1). It consists of threeboards:

Figure 3 CASES Receiver in Two Form Factors [5]

• RF Front End

• Digital Signal Processor (DSP)

• Interface Board (Z-board)

The RF front end, developed by Dan Bobyn Engineer-ing, Ltd., down-converts L1 and L2 signals to an inter-mediate frequency of 298.73 MHz, samples at 5.714286MHz, and quantizes the digital signal using two-bitquantization (sign and magnitude) [6]. It accepts asingle antenna input, as well as an optional externalclock reference input. In the absence an external clockreference, the front end uses an internal Temperature-Controlled Crystal Oscillator (TCXO).

The quantized digital signal is then fed into a repro-gramable, 1 GHz Texas Instruments C6457 DSP boardfor processing [7]. The DSP, using the GRID code de-scribed in the previous section, is responsible for ac-quiring and tracking GPS L1 and L2 signals, comput-ing pseudorange, Doppler, and carrier phase observ-ables, and computing a navigation solution from theobservables. The processed channel data, along withthe navigation solution, are then output through theZ-board to a satellite’s on-board computer.

Software Changes

Because the GRID software was originally de-signed to run on a static, terrestrial receiver, severalfundamental changes needed to be made before itcould be used on FOTON. These software changes,like the hardware reconfiguration, were also made bythe Radionavigation Laboratory.

The first change that needed to be made was wideningthe Doppler search window. Terrestrial receivers withTCXOs typically see up to 6 kHz Doppler, caused bythe motion of the GPS satellite and the drift rate of thereceiver’s TCXO. The Doppler observed by receivers inLEO, however, is dominated by the receiver’s dynam-ics, and can be as high as 40 kHz. Without wideningthe Doppler window, FOTON would not be able totrack signals in LEO.

Another important change was in the navigation solu-tion algorithm; because GRID was designed for staticreceivers, it uses a position averaging filter to attainsub-meter level accuracy. This must be turned off,however, for any dynamic scenarios, including LEO.Several other changes were made to the GRID in theprocess of making it space-capable, but as they weremore general updates only indirectly related to FO-TON, they will not be discussed.

3 CHARACTERIZATION OF CASES ANDFOTON

This section presents the initial characterization anddevelopment testing of the CASES and FOTON re-ceivers. This not only illustrates how tightly coupledtesting and development were in the project, but italso provides proper perspective for understanding theresults of testing presented in later sections. First,an overview of the testing setup and procedures isgiven, including a brief description of the hardware.Next, the results of testing the CASES receiver arepresented; these act as a baseline for evaluating the

performance of changes made to the code during earlyFOTON development. Finally, the initial characteri-zation of the FOTON receiver is presented. The lasttest in this section is a recreation of the LEO bench-mark test developed by Holt [8]. Thanks to the pre-viously documented results of this same test on otherreceivers [9], FOTON’s performance can be directlycompared with other space-based receivers.

3.1 Setup and Procedures

There are two basic types of tests that were performed:live sky tests and simulations. Although some live skytesting is presented to verify that the receiver does,in fact, work properly with live data, the majorityof testing presented used simulated signals. Simula-tions comprise static terrestrial, dynamic terrestrial,low earth orbit, and high earth orbit/geosynchronous(GEO) tests.

Live-Sky Testing

The live sky tests were conducted using a staticGPS antenna on the roof of the W. R. WoolrichLaboratories building at the University of Texas atAustin. The signals were transmitted via coaxialcable to the CASES receiver, and the output fromCASES was transmitted to a seperate computer foranalysis.

Simulator Setup

The Spirent GPS signal simulator is located atthe Center for Space Research (CSR) GPS labo-ratory, and can be set up to simulate a variety ofscenarios, from a stationary receiver to a receiverin orbit. The simulation scenario is defined on anadjacent computer. Different parameters can bevaried, including simulated antenna gain patterns andGPS constellation parameters. The simulator canalso simulate atmospheric effects, such as ionosphericand tropospheric delay. The tests presented in thissection, however, have these effects turned off. Theintent is to test the receiver’s base performance tocompare with other receivers. The simulator alsosaves a log file containing the simulated position,velocity, and time, as well as satellite position andobservables.

The output of the simulator is the (nearly) analog sig-nal that would be output from a receiver antenna, asdefined in the simulation scenario. A coaxial cableconnects the simulator’s RF output to the receiver’santenna input. A coaxial splitter is also used to input

the same signal to a device called a “bitgrabber”. Thebitgrabber consists of a Bobyn front end (the same asFOTON’s front end) connected to an Acces-IO USB-DI16A data acquisition board [10]. This board trans-mits the digitized IF data from the front end throughUSB to a computer or hard drive for storage. Record-ing simulations in this way allows for quick testing ofchanges to the software without having to go back toCSR’s GPS lab to re-run the tests.

3.2 CASES Receiver Testing

Before presenting the results of the FOTON charac-terization, three tests on the CASES receiver are pre-sented: a live-sky test, a static simulation, and a LEOsimulation.

Live-Sky Test

Approximately 20 minutes of live-sky data wasrecorded using the CASES receiver with the defaultGRID configuration. The average position andvelocity over the 20 minute interval is subtracted toobtain approximate position and velocity residuals,shown in the following two figures.

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Figure 4 CASES Live-Sky Position Residuals

The default GRID configuration uses a position av-eraging filter to improve position precision over time;the effect of this filter is seen in Figure 4 as the posi-tion residuals “walk”, rather than exhibiting Gaussianvariations as do the velocity residuals (Fig. 5). Thenon-Gaussian behavior of the position residuals couldalternatively be explained by multipath or some othertime-correlated phenomenon; however, the averagingfilter would most likely dominate other such effects.The 1-σ error in position and velocity is summarized

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Figure 5 CASES Live-Sky Velocity Residuals

in Table 1. After only 20 minutes, the positioning errorwas less than 2 meters. Greater precision is possiblewith longer position averaging times.

Table 1 CASES Live-Sky 1-σ Error

X Y Z || · ||Position [m] 0.377 1.541 0.744 1.753

Velocity [m/s] 0.013 0.022 0.017 0.031

Static Test

The static simulation scenario simulated the re-ceiver at 30◦ N, 97◦ W, and included both ionosphericand tropospheric delays. Like the live sky test, theCASES receiver was used with the default GRID con-figuration, including the position averaging. Figure 6shows the position filter converging toward the truesolution over the course of the 2-hour simulation.The spikes in the plot result from changes in thetracked GPS satellites, which can be seen as changesin position dilution of precision (PDOP). Also shownin this figure is the ratio of RMS error to PDOP,which is normally used to calculate user range error(URE). However, URE is based on the assumption ofa normally-distributed position error; because of theposition filtering, URE cannot be calculated.

LEO Test

The purpose of this test was to see how theGRID code, without any changes from the defaultconfiguration, would perform in a LEO scenario.The simulator was set up with a typical 90 minutelow earth orbit (specifically that of the InternationalSpace Station [11]), and the simulation logging set torecord the observables for all GPS satellites simulated.As expected, the receiver was not able to track enough

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Figure 6 CASES Static Simulation RMS Error andPDOP

satellites to obtain a navigation solution; however, itwas able to track 1-3 satellites at a time. The primarytracking constraint was Doppler: GRID, by default,can only track Doppler on the range of +/- 10 kHz(see Fig. 7). Contrast this figure with the actualDoppler simulated (Fig. 8); the actual simulatedDoppler is on the range of +/- 40 kHz.

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Figure 7 LEO Tracked Doppler History

3.3 FOTON Receiver Testing

After some required software changes to GRID, includ-ing the widening of the Doppler tracking window, theFOTON receiver was ready for testing. The first twotests were terrestrial: a static simulation and a sim-ple rectangular track simulation. These tests were in-tended to verify that FOTON performed as expected

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Figure 8 LEO Simulated Doppler History

for a terrestrial receiver before attempting LEO po-sitioning. These tests revealed a difference betweenthe real-time receiver and PpRx, uncovering a bug inthe SBC code, which was quickly located and fixed.Once the real-time receiver performed the same asPpRx, the code could be tested using an establishedLEO benchmark test. This test allows FOTON tobe directly compared with other space-based GPS re-ceivers, including the Orion single-frequency receiverused by small satellites in the past and the Jet Propul-sion Laboratory’s (JPL) dual-frequency BlackJack re-ceiver, which has previously been used in major sciencemissions.

Static Test

The static test was a repeat of the CASES staticsimulation, but without the atmospheric delays. Be-cause this test is only used to demonstrate the basicfunctionality of the receiver, it was only 15 minuteslong. The position and velocity residuals from thestatic simulation are shown in Figure 9. There was a0.41 m overall bias in position, with a 0.46 m standarddeviation. The velocity was zero-mean, with a 1-σerror of 0.035 m/s.

Rectangular Track Test

The rectangular track test simulated the receivertraveling around a terrestrial track at velocities andaccelerations of a tyipcal car. This test demonstratesFOTON’s capabilities to accurately track a receiverundergoing relatively slow terrestrial dynamics.Figure 10 shows the simulated trajectory in ECEFcoordinates.

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Figure 9 FOTON Static Simulation Residuals

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The RMS position and velocity errors are shown inFigure 11. Both position and velocity were nearlyzero-mean, with 1-σ errors of 0.83 m and 0.12 m/s,respectively.

LEO Benchmark Tests

In 2002, Holt developed a LEO simulation specificallydesigned to test receiver performance under a varietyof relative dynamics and signal levels [8]. The 2 hoursimulation consists of a nearly polar orbit containingsix pairs of GPS space vehicles (SVs) specificallychosen according to their relative dynamics andsignal levels. This simulation uses L1 C/A only, anddoes not simulate ionospheric or tropospheric effects.It also does not include any ephemeris errors. Byremoving these sources of error, this simulation makespossible an analysis of raw observable noise.

The analysis consists of a series of double differencecalculations using specified pairs of SVs and the “true”

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Figure 11 FOTON Rectangular Track RMS Errors

observables provided by the simulator log file. Thisprocess is illustrated in Figure 12. Because atmo-spheric delays are not simulated, the pseudorange, car-rier phase, and Doppler (pseudorange rate) observ-ables consist of only range, range rate, receiver and SVclock errors, and a constant phase ambiguity (moduloone wavelength). The first difference is between thecomputed observables and the simulator log file foreach SV; this removes all terms except for the receiverclock errors and the phase ambiguity. The resultingdifferences are then differenced again, removing thereceiver clock errors. All that remains is the observ-able noise, assumed to be zero-mean Gaussian, and thephase ambiguity. Since the phase noise is much lowerthan one wavelength (about 19 cm), the mean of thephase double difference, modulo one wavelength, canbe subtracted out to obtain the zero-mean Gaussianphase error.

Figure 12 Observable Double Difference [8]

Note that it does not actually matter if the receiver-simulator differences are made first, or if the SV-SVdifferences are made first. However, in this analysis itwill be assumed that the receiver-simulator differencesare first, followed by an SV-SV difference. As an ex-ample, the carrier phase double difference is outlinedbelow:

∆Φj = Φjrx − Φjsim

= cδtr + λN j + njΦ (1)

∆Φk = Φkrx − Φksim

= cδtr + λNk + nkΦ

∇∆Φjk = ∆Φk −∆Φj

= λ(Nk −N j) + nkΦ − njΦ (2)

σ2∇∆Φ = σ2

Φ + σ2Φ

= 2σ2Φ (3)

Here, Φ = λφ is the carrier phase expressed in meters,N j and Nk are the integer phase ambiguities of SVs jand k, respectively, and njΦ and nkΦ are the observablenoise terms. Note that it is assumed here that thesimulator noise is negligible compared to that of thereceiver, and that the receiver noise is independent ofSV, so that the double difference noise is a factor of√

2 greater than the actual observable noise.

The six SV pairs, along with the times in which bothSVs are visible to the receiver, can be found in Ref. [8].The results from the last double difference test areshown in Figure 13 as an example.

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The final test results are summarized in Table 2. Notethat test 3 is not shown; this is because the simula-tor log file did not include one of the SVs required by

Table 2 LEO Benchmark Testing Observables Noise

Test Observable FOTON Architect Orion BlackJack NovAtelPR [m] 0.1455 0.9258 0.9477 0.1553 0.0991

1 Phase [mm] 0.5286 0.9323 0.9253 0.5030 1.1970PR Rate [m/s] 0.0503 0.1407 0.1414 0.0010 0.0745

PR [m] 0.1449 0.9037 0.9193 0.1025 0.11212 Phase [mm] 0.5734 0.9227 1.0890 0.4270 1.2567

PR Rate [m/s] 0.0537 0.1382 0.1440 0.0010 0.0359PR [m] N/A 0.9015 0.9559 0.1323 0.1226

3 Phase [mm] N/A 1.0899 1.0699 0.4105 1.3715PR Rate [m/s] N/A 0.1419 0.1561 0.0010 0.0351

PR [m] 0.1548 0.9131 0.9029 0.1539 0.12674 Phase [mm] 0.6805 1.1566 1.6478 0.9524 1.3559

PR Rate [m/s] 0.0649 0.1526 0.1512 0.0010 0.0426PR [m] 0.1708 0.8986 0.8960 0.1606 0.1217

5 Phase [mm] 0.5784 1.1864 1.7767 0.6380 1.3480PR Rate [m/s] 0.0552 0.1469 0.1473 0.0010 0.0565

PR [m] 0.1920 0.9297 0.8942 0.1242 0.12856 Phase [mm] 0.6255 1.2112 1.5659 0.2833 1.4228

PR Rate [m/s] 0.0605 0.1466 0.1534 0.0010 0.0401PR [m] 0.1616 0.9121 0.9193 0.1381 0.1185

Average Phase [mm] 0.5973 1.0832 1.3458 0.5357 1.3253PR Rate [m/s] 0.0569 0.1445 0.1489 0.0010 0.0475

this test. Both SVs were simulated, as is evidenced bythe fact that the receiver tracked both signals, howeverthe log file only recorded a certain number of simulatedSVs, and either SV 3 or 15 was not recorded between177400 and 178900 seconds. This table shows that FO-TON’s performance is a significant improvement overthe Architect and Orion receivers, though not quite asgood as the BlackJack or NovAtel. These receivers,however, likely use time averaging of observables toimprove performance, a technique not currently im-plemented on FOTON.

4 ON-ORBIT ACQUISITION AND REAC-QUISITION

In order to use FOTON on small satellites such asCubeSats, it is necessary to duty cycle the receiverdue to power consumption constraints. While FOTONruns on an average of 4.5 W [12], a typical CubeSathas a total power budget of less than 10 W; it wouldnot be feasible to use half of the total power for a sin-gle sensor. By only running FOTON for 1/3 of thetime, however, its orbit-average power consumptioncan be reduced to 1.5 W. Since the receiver will onlybe active for short periods of time, it must be ableto quickly acquire signals and begin reporting naviga-tion solutions as soon as it is turned on. This sectionexamines the time it takes to track enough signals to

compute a navigation solution (time to first fix). Inaddition, several loss-of-signal scenarios are examinedto show FOTON’s signal reacquisition capabilities.

The scenario consists of the same polar LEO simula-tion used in the benchmark tests of section 3. Duringthe simulation, six events simulate various types of sig-nal loss or duty cycling; each event is separated by sev-eral minutes of tracking to allow the receiver to fullyrecover a position solution. First, 6 minutes into thesimulation, the simulated spacecraft performs a slow(6 minute duration) 360◦ roll. Next, the antenna is de-tached for 60 seconds, then reattached. Another roll isperformed when the spacecraft is near the north pole(2 minute duration). The next two events are systemresets, followed by a complete system reboot.

The six events are illustrated in Figure 14 as gaps inthe navigation solution. Note the large increase inresiduals for the 360◦ rolls (the 1st and 3rd events);this is due to the gradual degradation of receiver-satellite geometry during the rolls.

4.1 Time to First Fix

The time to first fix is the time it takes for the receiverto obtain a valid navigation solution, measured fromthe moment the receiver is turned on. Time to first

1.725 1.73 1.735 1.74 1.745 1.75 1.755

x 105

0

1000

2000

3000

|δr|

(m

) ← Roll 1

← Unplug Ant

← Roll 2

← Soft Reset

← Hard Reset

← Reboot

1.725 1.73 1.735 1.74 1.745 1.75 1.755

x 105

0

100

200

300

400

500

|δv| (m

/s)

1.725 1.73 1.735 1.74 1.745 1.75 1.755

x 105

−100

0

100

Time (sec of week)

Ro

ll (d

eg

)

Figure 14 Acquisition Simulation Residuals

fix varies depending on DOP and acquisition searchdepth, but on average, FOTON’s time to first fix isabout 45-50 seconds.

4.2 Six Minute Roll

The six minute roll began 5 minutes into the simula-tion. As can be seen in Figure 14, the receiver didnot undergo a constant roll rate, but rather a morerealistic spin-up and spin-down roll, with an averagerate of 1 deg/sec. The receiver lost the navigation so-lution 185 seconds into the roll, and lost track of thelast signal 200 seconds into the roll. In reality, thereceiver could no longer see signals at at 180 secondsinto the roll, because this was the half-way point whenit was earth-pointing. However, the receiver continuesto attempt to track signals that have disappeared untiltheir low signal level identifies them as “ghost signals”.FOTON reacquired the first signal on the later half ofthe roll at 211 seconds into the roll, that is, 31 secondsafter the antenna was earth-pointing. The first validnavigation solution was obtained 47 seconds later; thetotal gap between valid navigation solutions was ap-proximately 73 seconds.

4.3 Antenna Disconnect

Sudden loss of all signals was simulated by disconnect-ing the coaxial cable that connected the simulator tothe receiver. This was done at a simulation time of 15minutes, 3 minutes after the completion of the previousevent. This 3 minute buffer ensured that the receiverhad returned to normal operation. After the cablewas disconnected, the receiver continued to track ghost

signals for 20 seconds before they were all “pruned”.After 60 seconds, the cable was reattached, and thereceiver began tracking signals again 2 seconds later.A valid navigation solution was obtained 44 secondslater.

4.4 Two Minute Roll

The two minute roll was started 21.5 minutes into thesimulation, 5.5 minutes after the previous event. Thistime was chosen so that the receiver would be approx-imately at the north pole at the time of the roll, sothat in addition to the roll dynamics, the satellite ge-ometry would be challenging as well. Because this rollwas much quicker than the previous one (3 deg/secaverage), the receiver never actually lost track on allsatellites. It tracked ghost signals until real ones be-came visible. However, there was a 50 second gap inthe navigation solution, from 1 minute into the roll(when the antenna was earth-pointing) to 10 secondsbefore the end of the roll. Even with the faster roll,however, the receiver still recovered a valid navigationsolution before the roll was complete.

4.5 Soft and Hard Resets

Two reset commands can be issued to FOTON’s DSP:a soft reset and a hard reset. Although this structuremakes room for future functionality, at present bothcommands are exactly the same, and hereafter will bereferred to simply as a reset. The next two events,again separated by 5 minutes to allow the receiverto fully recover, were a soft and hard reset, respec-tively. As expected, both commands performed thesame DSP reset, and took the same amount of time. Ittook 17-18 seconds from the time the command was is-sued to regain tracking of the first signal, and another30 seconds after that until the first valid navigationsolution. The antenna-disconnect event demonstratedthat the receiver only takes a few seconds to actuallyacquire a signal, so the reset time is then approxi-mately 14-15 seconds.

4.6 SBC Reboot

Whereas the soft and hard resets only reset the DSP,a reboot actually shuts down the DSP and reboots theSBC (single board computer). The reboot was com-manded 5 minutes after the second DSP reset, andtook about 46 seconds until the first signal was tracked,

and another 32 seconds until the first navigation solu-tion. Allowing 15 seconds for the DSP to reset, it takesabout 30 seconds for the SBC to reboot. The SBC,however, would be replaced by a satellite’s on-boardcomputer, so the SBC reboot time has no bearing onFOTON’s reset time.

4.7 Summary

FOTON’s DSP only takes about 15 seconds to reset,after which it immediately begins acquiring new sig-nals. Allowing 30 seconds for ephemeris retrieval fromthe nav message, the time to first fix is still under oneminute. This time can be further reduced by storingephemerides in memory, and by running the DSP inlow-power mode to reduce the time it takes to reset.With these modifications, the time to first fix can bereduced to just a few seconds, maximizing the amountof useful on-duty time.

5 KALMAN FILTER-BASED PRECISEORBIT DETERMINATION

The results presented until now have used a standardleast-squares iterative solution based on the pseudo-range and Doppler observables from each tracked SV[13]. In static scenarios, these basic point solutions canbe averaged to improve overall precision. Similarly indynamic scenarios, an Extended Kalman Filter (EKF)can be used to incorporate a time history of observ-ables into a more precise navigation solution. Thissection outlines a basic orbital EKF for FOTON thatimproves on the default point solutions, making pos-sible on-board, sub-meter precise orbit determination(POD) after a sufficient improvement of the dynamicsmodel fidelity.

5.1 State Dynamics

The receiver’s state consists of Earth-Centered, Earth-Fixed (ECEF) position r and velocity v, and clock biasδtR and rate δtR:

x =

r

cδtRv

cδtR

(4)

where the speed of light c is used to express the clockterms in equivalent meters and meters per second (forunit consistency with the position and velocity states).

The receiver clock bias is defined as the difference be-tween the receiver time and true GPS time (TGT):

δtR = tR − tGPS (5)

This EKF will be based on true GPS time rather thanreceiver time, so all time derivatives will be with re-spect to TGT.

The state differential equation model is then

f = x =

v

cδtR + uta + uvuf

(6)

where a is the total acceleration in the ECEF frame,and uv, ut, and uf are uncorrelated, zero-mean, white-noise processes with covariances given by

Qv = E[uvuTv ] = σ2

vI3×3 (7)

σ2t = E[ut(t)ut(τ)] =

1

2h0c

2δ(t− τ) (8)

σ2f = E[uf (t)uf (τ)] = 2π2h−2c

2δ(t− τ) (9)

Here, h0 and h−2 are constant parameters (units of secand 1

sec , respectively) used to characterize a receiver’sclock stability [14], and δ(t− τ) is the Kronecker deltafunction (units of 1

sec ). The velocity process noise σvwill serve as a filter tuning parameter.

The ECEF acceleration term in Equation 6 can beexpressed in terms of the ECI acceleration:

a = g + 2ωe

vy−vx

0

+ ω2e

xy0

(10)

where g is the total acceleration in the ECI referenceframe. For now, a simple J2 gravity model [15] will beused, with no atmospheric drag. For a full derivation,including linearization and covariance propagation, seeRef. [16].

5.2 Measurement Models

This orbital EKF uses pseudorange and pseudorangerate observables in its measurement updates. Whilethe pseudorange is a raw observable, the pseudorangerate is not; it is derived from Doppler. Since the onlydifference between pseudorange rate and Doppler isa constant scaling, however, the pseudorange rate istreated as a raw observable.

Pseudorange

The pseudorange model consists of the true range rk

to the kth SV, the receiver clock bias δtR, the SVclock bias δtkS , tropospheric T k and ionospheric Ik

delays, and noise nkρ:

ρk = rk + c(δtR − δtkS) + Ik + T k + nkρ (11)

The noise in the pseudorange measurement can be es-timated as a function of signal carrier-to-noise ratioC/N0:

σ2ρ =

dBDLLT2c c

2

2 CN0

[m2] (12)

where d = teml

Tcis the DLL correlator’s early-minus-

late chip spacing, Tc is the chip length (1 ms for GPSL1 C/A), and BDLL is the DLL bandwidth in Hz.

Pseudorange Rate

The pseudorange rate is derived from the Dopplerobservable as follows:

ρ = −λfD = −cfDf0

(13)

Where f0 and λ are the L1 frequency and wavelength,respectively, and fD is the observed Doppler shift ofthe received signal. The negative sign is introducedbecause the Doppler shift is positive for approachingSVs, when the range rate is negative. A model for thepseudorange rate based on the current state involvesthe relative velocity vr along the line-of-sight vector `,the receiver clock rate δtR, and the satellite clock rateδtS :

ˆρ =

[cδtR − cδtS − vr(1 + δtS)

(1 + δtS)(c+ vr)

]c (14)

where vr is the line-of-sight velocity, or the negative ofthe range rate.

The noise in the pseudorange rate measurement canbe estimated from carrier phase noise, a function ofC/N0, PLL bandwidth Bn, and the accumulation in-terval Tacc (part of the squaring loss SL term).

σ2φ =

BnCN0SL

rad2 (15)

S−1L = 1 +

1

2TaccCN0

(16)

Doppler can be approximated with a single-differenceof phase, which leads to the pseudorange rate noise

estimate.

fD = − ρλ≈ φ2 − φ1

2πTacc(17)

ρ ≈ − λ

2πTacc(φ2 − φ1) (18)

σ2ρ ≈

2σ2φλ

2

(2πTacc)2(19)

σ2ρ ≈

2λ2BnCN0SL(2πTacc)2

m2/sec2 (20)

5.3 EKF Results

The EKF was tested using the same polar LEO simu-lation as in previous sections. The EKF is initializedwith the first point solution obtained (about 45 sec-onds into the simulation), with a diagonal initial co-variance, with σr0 = σt0 = 0.5 m and σv0 = σf0 =0.1 m/s. These values are based on the approximatenoise apparent in the standard point-wise navigationsolution. The filter was tuned by varying the veloc-ity process noise σv; the value that produced the bestresults was σv = 0.001 m/s2. The clock noise termswere calculated using h−2 = 2.9 × 10−21 sec−1 andh0 = 3.4 × 10−21 sec; these parameters were empiri-cally computed by Kassas and Pesyna of the Radion-avigation Laboratory for the TCXO used in FOTON’sRF front end.

The position residuals are shown in Figure 15. Al-though the EKF noticeably reduces the noise in theposition solution as compared with the point-wise so-lutions, it does not reduce the overall bias. This isbecause the EKF gravity model only includes J2 ef-fects, whereas the simulator used a 10th order gravitymodel. The velocity, on the other hand, is nearly zero-mean, with an order-of-magnitude reduction of noise.

There is no way to directly measure clock error, sothe best that can be done is to compare the clock biasand rate with the values obtained by the point-wisesolutions computed at the same time. The differencein bias and rate (in equivalent meters and meters persecond) is shown in Figure 16. It should be noted,however, that most of the noise shown is from the pointsolution; this can be seen in Figure 17, which showsthe point-wise and EKF solutions for the clock rate.The EKF solution has much lower noise than the pointsolution. The results of the EKF vs. point solutioncomparison are summarized in Table 3.

Table 3 EKF and Point-Wise Residuals

Solution Position [m] Velocity [m/s] ClockType Mean Std Mean Std Bias RateEKF 0.174 0.544 1.22× 10−4 0.0121 0.432 m 0.157 m/sPoint 0.122 0.739 0.0812 0.247 N/A N/A

Figure 15 EKF Position and Velocity Residuals

6 DUAL-FREQUENCY CAPABILITY

Designed specifically to be an ionospheric sensor, theCASES receiver was already set up to process dual-frequency measurements. Although FOTON will alsouse its dual-frequency capability to directly measureionospheric delay during satellite occultations, thissection will focus on using the L2C signal to negatethe effect of ionospheric delays to improve the naviga-tion solution.

The Spirent simulator at UT-Austin that was used inprevious tests is incapable of simulating L2C signals,so it could not be used for dual-frequency testing. For-tunately, Cornell University, one of the collaboratorson the CASES receiver, has a newer Spirent device

Figure 16 EKF - Point Solution Clock Residuals

Figure 17 EKF cδtR Solution

that does simulate L2C. O’Hanlon of Cornell used thenewer simulator to record a dual-frequency, LEO sim-ulation similar to the previously tested baseline po-lar orbit. In this simulation, L2C was simulated onall satellites. Currently, there are only 9 L2C-capableGPS satellites on orbit; however, the limited number ofL2C-capable satellites can still be simulated by speci-fying in FOTON’s configuration file which satellites toattempt to track. Also note that the simulated iono-sphere was based on the standard Klobuchar model.

6.1 Dual-Frequency Ionospheric Delay Esti-mation

Most dual-frequency receivers directly eliminate theionospheric delay for L2C-capable SVs by forming ameasurement known as the “ionosphere-free” pseudo-range:

ρL1 = ρL1 −f2L2

f2L2 − f2

L1

(ρL1 − ρL2) (21)

=f2L1ρL1 − f2

L2ρL2

f2L1 − f2

L2

FOTON, however, does not use this ionosphere-freepseudorange. Instead, it uses the L1 and L2 pseu-doranges from L2C-capable SVs to update a runningestimate of vertical TEC (TECV). Satellite elevationis then used to map the TECV to a slant TEC forL1-only SVs as well as L2C-capable SVs. Not onlydoes this method improve the estimate of ionosphericdelay for L1-only satellites as well as L2C-capableones, but it also acts as a filter on the ionosphericdelay estimates, reducing noise. This works very wellfor stationary receivers (such as FOTON’s predeces-sor CASES), but it may present problems for LEO re-ceivers. For instance, while TECV changes slowly forstationary receivers, it will change more rapidly forLEO receivers. In this case, independent, point-wiseestimates of ionospheric delay may be more accurate,albeit more noisy, than filtered estimates.

6.2 LEO Simulation Testing

Once the interfrequency bias was determined, FOTONwas tested using four different configurations. Thebaseline configuration (case 1) tracked L1 only, andinitialized the Klobuchar model parameters with theactual parameters used in the simulation (also in thebroadcast ephemeris). By initializing the Klobucharparameters with the values used in the simulator fromthe beginning of the simulation, the receiver’s iono-spheric model is exactly matched with the simulator’smodel. This baseline case, then, should be more accu-rate than even dual-frequency configurations. Case 2also tracked L1 only, but it initialized the Klobucharparameters with the default null values; this demon-strates the receiver’s default single-frequency perfor-mance in the presence of ionospheric delays. Case 3tracked L1 and L2 on all satellites. This shows whatperformance can ultimately be expected as the GPSconstellation is modernized. Case 4 also tracked L1and L2, but restricts the L2 signals tracked to the 9PRNs that currently transmit L2C. The results here

presented were from the standard point-wise naviga-tion algorithm; each case was also tested with theKalman filter, but due to the low-fidelity dynamicsmodel, sub-meter precision was not attained.

The position residuals from the case 1 are shown inFigure 18. Note the increase in noise near the end ofthe simulation; this was when the receiver was passingover the north pole, so DOP was higher.

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−2

0

2

4

∆x (

m)

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−1

−0.5

0

0.5

1

∆y (

m)

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−10

−5

0

5

∆z (

m)

GPS SOW

Figure 18 Position Residuals, L1-Only, InitializedKlobuchar Model (Case 1)

Comparing this with case 2 (Fig. 19), the positionresiduals for the single-frequency configuration withuninitialized Klobuchar parameters, reveals a large ini-tial error that is corrected about 8 minutes into thesimulation. In this configuration, the Klobuchar modelis initialized with null parameters, so the estimatedionospheric delay is zero. Once the Klobuchar parame-ters have been received from the broadcast ephemeris,however, the model is updated, and the ionosphericdelays are properly estimated. After this correction,the residuals follow the same trends as the baselineconfiguration.

The position residuals for case 3 are shown in Fig-ure 20. As expected, the errors are very similar tothe baseline configuration (Fig. 18). Because of theway FOTON filters the L2C measurements to estimatethe ionospheric delay for L1-only SVs as well as L2C-capable ones, the reduction in performance in case 4(with limited number of L2C signals tracked) is mini-mal (Fig. 21).

Table 4 summarizes the position and velocity residualsfor all four configurations. As expected, the best con-figuration was the baseline; however, this is only be-cause the receiver exactly matched ionospheric modelswith the simulator. The first half of case 2 is more

Table 4 Position and Velocity Point Solution Residuals

Position [m] Velocity [m/s]Mean 1-σ Mean 1-σ

L1, Init. Params 0.7650 1.1520 0.0657 0.3035L1, Uninit. Params 1.8520 2.2786 0.0661 0.3094DF, All L2C 1.1040 1.4711 0.0628 0.2920DF, Limited L2C 1.1190 1.2749 0.0612 0.3048

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−2

0

2

4

6

∆x (

m)

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−2

−1

0

1

2

∆y (

m)

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−5

0

5

10

∆z (

m)

GPS SOW

Figure 19 Position Residuals, L1-Only, UninitializedKlobuchar Model (Case 2)

representative of single-frequency performance. Thetwo dual-frequency configurations were nearly identi-cal; this is because of the filtering method currentlyemployed to estimate the ionospheric delays. Notethat the velocity residuals for all four configurationsare essentially the same. This is because the standardpoint-wise navigation algorithm used in these testscomputes velocity using Doppler only, and is indepen-dent of pseudorange, and thus ionospheric delay.

A comparison of these results with the single-frequencytest results of Chapter 3 reveals a degradation in per-formance. This is clearly due to the presence of iono-spheric delay on the pseudorange. However, sub-meteraccuracy of the dual-frequency solutions is still attain-able by including the raw L2 pseudorange in a Kalmanfilter that is designed to process dual-frequency mea-surements. This capability, however, has yet to bedeveloped.

7 RADIO OCCULTATION OBSERVATION

In most terrestrial scenarios, GPS signals are receivedfrom relatively high elevation. In these cases, the sig-nals travel through the ionosphere and troposphere

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−2

0

2

4

∆x (

m)

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−1

0

1

2

∆y (

m)

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−10

−5

0

5

∆z (

m)

GPS SOW

Figure 20 Position Residuals, Dual-Frequency, AllL2C (Case 3)

more or less perpendicularly, passing through all ofthe layers before reaching the receiver. If the receiveris in LEO, however, it can track signals below the hori-zon; this happens as GPS satellites set behind the LEOsatellite, because its velocity is much higher than thatof the semi-synchronous GPS satellites. When this oc-curs, signals pass horizontally through the ionosphericand tropospheric layers (Fig. 22); such an event isknown as an occultation.

By using dual-frequency measurements, the slant totalelectron count (STEC or just TEC) along the signalpath during an occultation can be directly computed.As the SV sets, the signal travels through more layersof the ionosphere, and the TEC increases. CompleteTEC profiles during occultations can be used to mapthe ionosphere and monitor space weather. At lowenough elevations, delay through the troposphere canalso be calculated and used to compute density pro-files, which can then be used to improve terrestrialweather models.

Several missions have been devoted entirely to radiooccultations. The currently-operational COSMIC mis-sion, for example, uses a small constellation of satel-lites with high-precision GPS receivers to observe oc-cultations world-wide [3]. With the small, low-power

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−4

−2

0

2

4

∆x (

m)

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−1

−0.5

0

0.5

1

∆y (

m)

9 9.02 9.04 9.06 9.08 9.1 9.12 9.14 9.16 9.18

x 104

−5

0

5

∆z (

m)

GPS SOW

Figure 21 Position Residuals, Dual-Frequency, Lim-ited L2C (Case 4)

Figure 22 Radio Occultation [3]

FOTON receiver, a similar mission could be performedwith a larger constellation of much smaller CubeSats.Such a mission would provide even greater world-widecoverage than COSMIC at a fraction of the expense.

7.1 Occultation Observation in a LEO Simu-lation

The dual-frequency LEO simulation from section 6contains a number of occultations of varying eleva-tions. To illustrate FOTON’s occultation observingcapability, the lowest-elevation SV tracked, PRN 13,was analyzed. FOTON acquired PRN 13 at an eleva-tion of 78◦, and tracked it until it set at an elevation of-15◦. The slant TEC, computed with the pseudorangemeasurements, is the noisy measurement shown in Fig-ure 23. The carrier-phase-derived TEC is the smoothline in this figure. Note, however, that carrier-phase-derived TEC is ambiguous, so it must be appropri-ately shifted to yield an accurate TEC measurement.If the pseudorange-derived TEC is denoted as TECρand the carrier-phase-derived TEC relative to zero isdenoted as δTECΦ, then the unbiased carrier-phase-

derived TEC, denoted TECΦ, is computed as

TECΦ(t) = δTECΦ(t) + E [TECρ(t)− δTECΦ(t)](22)

−20 −10 0 10 20 30 40 50 60 70 80−10

0

10

20

30

40

50

Elevation [deg]

Sla

nt T

ota

l E

lectr

on C

ount [T

EC

U]

PRCP

Figure 23 Slant TEC versus Elevation

Assuming a spherical Earth and a straight signal paththrough the ionosphere, the lowest altitude attianedby the signal can be computed from the elevation asfollows:

hmin = r cos(el)−Re (23)

where r is the norm of the LEO satellite’s position,Re is the Earth’s mean equatorial radius, and el is theocculting SV’s elevation. Note that these are not verygood assumptions; the Earth is better modeled withan equatorial bulge, and the signal is bent as it travelsthrough the ionosphere. However, these simplifyingassumptions allows the elevation in Figure 23 to bemapped to altitude, shown in Figure 24, which illus-trates that FOTON was able to track PRN 13 until itwas blocked by the Earth itself.

This short example demonstrates that FOTON can beused effectively as an occultation sensor, even aboarda CubeSat. The relatively small expense of FOTON,combined with its small size and low power require-ments, could make large-scale CubeSat occultationmissions feasible.

8 HIGH ALTITUDE AND GEOSYN-CHRONOUS ORBITS

Up to this point, testing and development of FOTONhas been based on the assumption that the receiver

−50 0 50 100 150 200 250−10

0

10

20

30

40

50

Min. Signal Altitude [km]

Sla

nt

To

tal E

lectr

on

Co

un

t [T

EC

U]

PR

CP

Figure 24 Slant TEC versus Altitude

is in LEO. However, many satellites are placed inhigh Earth orbits (HEO), particularly geosynchronous(GEO). With a semi-major axis of 42164 km, GEOsatellites are well outside the GPS constellation. Al-though GPS signals are directed toward the earth, thetransmitters were designed with a slightly wider beamthan is necessary for Earth coverage; as a result, areceiver in HEO or even GEO can still see some sig-nals that are not blocked by the Earth (Fig. 25). Inaddition, the GPS transmitting antenna gain patternincludes some lower-power side lobes that may be pos-sible to track. This section presents the results of pre-liminary GEO testing of the FOTON receiver.

Figure 25 HEO/GEO GPS Geometry [17]

8.1 GEO Simulation Setup

One challenge in setting up a GEO simulation is that,by default, the Spirent simulator assumes an isotropictransmitting antenna. This simplifying assumptionis inconsequential for terrestrial or even LEO simu-lations, but it is unacceptable for GEO. Fortunately,the simulator is adaptable enough to allow the userto input a gain pattern for the transmitting antennae.The gain pattern used in the simulation is shown inFigure 26.

0 20 40 60 80−40

−35

−30

−25

−20

−15

−10

−5

Zenith Angle (deg)

Rela

tive A

nte

nna G

ain

(dB

)

Figure 26 GPS Transmitting Antenna Gain Pattern[18]

As demonstrated by Moreau, the number of GPS satel-lites visible to a receiver in HEO/GEO is only occa-sionally four or more. Due to data storage limitations,a complete 24-hour simulation was not practical; in-stead, the GPS ephemerides for a specific epoch (inthis case, week 1139, 172800 seconds of week) werepropagated for 24 hours, and a two-hour window con-taining at least four visible satellites was selected. Thiswindow began at 244800 seconds of week 1139.

Unlike the previous tests in which FOTON used its

own internal TCXO clock, this time the receiver wasslaved to an external OCXO. This more stable clockallows a reduction in the PLL bandwidth, which de-creases the signal noise. This increases the receivedC/N0, which is essential to tracking weak signals inGEO.

8.2 Point-Wise Solutions

In order to acquire and track the weak signals expectedin GEO, FOTON was configured to perform 20 ms co-herent accumulation; this is the maximum allowableaccumulation interval without using data bit wipe-offtechniques. In addition, the Doppler search windowwas reduced to +/- 10 kHz because the receiver is ex-pected to be stationary (in the ECEF frame). Finally,the PLL bandwidth was also reduced to 10 Hz, furtherdecreasing noise levels.

As anticipated, the receiver tracked four signals formost of the two-hour simulation. The number of satel-lites tracked is shown in Figure 27; it varied fromtwo to four SVs. During the times when the receiver

0 1000 2000 3000 4000 5000 6000 7000 80002

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4

Time [sec]

# T

racke

d S

Vs

Figure 27 Number of Satellites Tracked

tracked four satellites it was able to compute a naviga-tion solution using the standard point-wise algorithm.Given the fact that DOP is one to two orders of mag-nitude higher in GEO, the residuals of these point so-lutions are relatively small (Fig. 28).

The already bad geometry appears to get even worsetowards the end of the simulation (after 5000 seconds),but for the first two periods of four-SV-visibility, thenavigation solution is relatively good. The error alongthe X-axis (the radial direction) is far worse than theerrors in the Y-Z horizontal plane. This is no surprise

0 1000 2000 3000 4000 5000 6000 7000 8000−500

0

500

∆x [

m]

0 1000 2000 3000 4000 5000 6000 7000 8000−50

0

50

∆y [

m]

0 1000 2000 3000 4000 5000 6000 7000 8000−50

0

50

∆z [

m]

Time [sec]

Figure 28 GEO Position Residuals

given the lack of geometric diversity in the X-direction.The errors for these first two data sets are given inTable 5.

Table 5 GEO Navigation Solution Residuals

X Y Z ‖r‖Position [m]

Mean: 18.281 1.276 -0.145 18.3261-σ: 155.3673 3.1213 7.9116 155.5999

Velocity [m/s]Mean: 2.3692 0.3665 0.1286 2.40081-σ: 14.92136 0.26513 0.68159 14.93927

8.3 Summary

By using an external OCXO to allow smaller a PLLbandwidth and using longer coherent accumulationtime to increase signal C/N0, FOTON is able to de-termine horizontal position in GEO to within 10 me-ters, and vertical position within 200 meters, withoutthe need of filtering. A properly tuned Kalman fil-ter would further enhance performance. Furthermore,due to the low signal dynamics present in GEO, evenlonger coherent accumulation times may be used, pro-vided the data bits are wiped off appropriately. Thiswill allow FOTON to pull in signals from transmitterside lobes in addition to the main lobes, making moreSVs visible, and further increasing GEO navigationperformance.

9 CONCLUSION

As satellites shrink in size and grow in navigationrequirements, the need for a small, low-power, dual-frequency, space-based GPS receiver becomes evident.As a software-defined receiver, FOTON has great po-tential for meeting this need.

Low Earth orbit single-frequency simulations showthat 0.5 m precision orbit determination is attainableby FOTON, with potential for better performance us-ing a Kalman filter. Dual-frequency LEO simulationsyield 1.5 m precision in the presence of ionosphericdelays; this could also be improved by implement-ing a Kalman filter that processes raw dual-frequencymeasurements rather than ionosphere-corrected single-frequency measurements.

With a time to first fix of approximately 45 seconds,FOTON could be duty-cycled to conserve power. Forexample, operating a total of 8 hours per day, it wouldconsume 1.5 W orbit average power instead of 4.5W. FOTON could operate less frequently if neededby relying on a high-fidelity Kalman filter to makeup for the fewer measurements. Because FOTONis a software-defined receiver, such settings could bechanged on-orbit.

Another advantage of FOTON’s versatility as asoftware-defined receiver is that, with slight modifi-cations to its configuration file and using an externalOCXO as a timing reference, FOTON can navigatein geosynchronous orbits. Tracking signals from theGPS transmitting antenna main lobe, FOTON is ableto navigate within 10 m horizontal and 200 m verticalprecision. With some additional modifications, suchas data bit wipe-off and long coherent accumulation,FOTON should also be able to track signals from thefirst side lobe. This would allow FOTON to track morethan four SVs, further increasing navigation precision.

In addition to FOTON’s potential for precise orbit de-termination in LEO and GEO, it could also be de-veloped into a radio occultation sensor. Capable oftracking signals down to the surface of the Earth, FO-TON could be modified to map tropospheric as wellas ionospheric profiles during occultations. This wouldallow such missions as COSMIC to be performed at afraction of the cost.

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